Busi.Statistics Exam 4

In a simple linear regression model, if the points on a scatter diagram lie on a straight line with a negative slope, which of the following is the coefficient of determination?

+1

A sample regression equation is given by yˆy^ = −100 + 0.5x. If x = 20, the predicted value of y is ________.

-90

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the standard error of the estimate?

0

In the following table, individuals are cross-classified by their age group and income level. Income Age. Low. Medium. High 21-35. 120. 100. 75 36-50. 150. 160. 100 51-65. 160 180. 160 Which of the following is the estimated joint probability for the "low income and 21-35 age group" cell?

0.0996

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Male. Female Candidate A. 150. 130 Candidate B. 100. 120 For the chi-square test of independence, the assumed degrees of freedom are ____.

1

The following is an incomplete ANOVA table. Source of Variation. SS. df. MS. F Between groups 2. 12.5 Within groups Total. 100. 10 The value of the test statistic is _______.

1.333

If there are five treatments under study, the number of pairwise comparisons is _______.

10

In the following table, individuals are cross-classified by their age group and income level. Income Age. Low. Medium. High 21-35. 120. 100. 75 36-50. 150. 160. 100 51-65. 160. 180. 160 Assuming age group and income are independent, the expected "low income and 21-35 age group" cell frequency is ________.

105.27

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race. Coordinator. Analyst. Manager. Director White. 32. 20. 25. 9 Black. 35. 10. 25 5 Hispanic. 32. 15. 13. 2 Asian. 10. 11. 10. 0 The column total for directors is _____.

16

The following is an incomplete ANOVA table. Source of Variation. SS. df. MS. F Between groups 2. 12.5 Within groups Total. 100. 10 The sum of squares due to treatments is _______.

25

Consider the following sample regression equation yˆy^ = 200 + 10x, where y is the supply for Product A (in 1,000s) and x is the price of Product A (in $). If the price of Product A is $5, then we expect supply to be ________.

250,000

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Credit Score Class. Less than 650. 650-750. More than 750 Income < $50,000 26 30. 24 $50,000 ≤Income < $100,000 63. 53. 44 $100,000 ≤ Income < $150,000 40. 30 30 Income ≥ $150,000. 21. 17. 22 The expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is ______.

26.0

1.b) A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below. Source of Variation. SS. df. MS. F Between groups 87.79. 3. 29.26. 9.12 Within groups. 64.17. 20. 3.21 Total 151.96. 23 The degrees of freedom for the hypothesis test are _______.

3,20

Consider the partially completed one-way ANOVA summary table. Source of Variation. SS. df. MS. F Between groups. 270 Within groups 18 Total. 810. 21 The value of the test statistic is ________.

3.0

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race. Coordinator. Analyst. Manager. Director White. 32. 20. 25. 9 Black. 35. 10. 25 5 Hispanic. 32. 15. 13. 2 Asian. 10. 11. 10. 0 The row total for Asians is _____.

31

In the following table, individuals are cross-classified by their age group and income level. Income Age. Low. Medium. High 21-35. 120. 100. 75 36-50. 150. 160. 100 51-65. 160 180. . 160 For the chi-square test of independence, the degrees of freedom are __________.

4

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Credit Score Class. Less than 650. 650-750. More than 750 Income < $50,000 26 30. 24 $50,000 ≤Income < $100,000 63. 53. 44 $100,000 ≤ Income < $150,000 40. 30 30 Income ≥ $150,000. 21. 17. 22 The degrees of freedom for the critical value is ________.

6

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race. Coordinator. Analyst. Manager. Director White. 32. 20. 25. 9 Black. 35. 10. 25 5 Hispanic. 32. 15. 13. 2 Asian. 10. 11. 10. 0 For the chi-square test for independence to be valid, Martha combines the seniorities Manager and Director. As a result, the degrees of freedom used are _____.

6

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Credit Score Class. Less than 650. 650-750. More than 750 Income < $50,000 26 30. 24 $50,000 ≤Income < $100,000 63. 53. 44 $100,000 ≤ Income < $150,000 40. 30 30 Income ≥ $150,000. 21. 17. 22 The expected number of individuals with income between $50,000 and $100,000 and a credit score less than 650 is ________.

60.0

7.a) A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0 + β1Age + ε. The following table summarizes a portion of the regression results. A CHART Which of the following is the estimate of Happiness for the person who is 65 years old?

75

The following is an incomplete ANOVA table. Source of Variation. SS. df. MS. F Between groups 2. 12.5 Within groups Total. 100. 10 For the within groups category, the degrees of freedom are _______.

8

AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. The following data represent the age of a random sample of trucks, cars, and vans. Trucks. Cars. Vans 12. 8. 3 8. 7. 7 9. 10. 6 11. 7. 8 The grand mean for these observations is ________.

8.0

The following is an incomplete ANOVA table. Source of Variation. SS. df. MS. F Between groups 2. 12.5 Within groups Total. 100. 10 The mean square error is _______.

9.375

The chi-square test of a contingency table is valid when the expected cell frequencies are _______________.

At least 5

5.a) A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the following model: Salary = β0 + β1 Service + ε. The following table summarizes a portion of the regression results. A CHART Using the 95% confidence interval, which of the following is the conclusion to the following hypothesis test: H0:β0 = 0; HA: β0 ≠ 0?

At the 5% significance level, reject H0 because the interval does not contain 0.

Suppose you want to determine if gender and major are independent. Which of the following tests should you use?

Chi-square test for independence

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race. Coordinator. Analyst. Manager. Director White. 32. 20. 25. 9 Black. 35. 10. 25 5 Hispanic. 32. 15. 13. 2 Asian. 10. 11. 10. 0 Which of the following is a way to ensure all expected frequencies in each cell of the above table are five or more?

Combine the expected frequencies for seniorities Manager and Director.

Consider the sample regression equation yˆy^ = 12 + 3x1 − 5x2 + 7x3 − 2x4. When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4remain unchanged, what change would you expect in the predicted y?

Decrease by 7

What is the name of the variable that is used to predict another variable?

Explanatory

One-way ANOVA assumes the population standard deviations are unknown and assumed unequal.

False

One-way ANOVA is used to determine if differences exist between the means of three or more populations under dependent sampling.

False

The between-treatments variance is the estimate of σ2 based on the variability due to chance.

False

Which of the following statements is TRUE about goodness-of-fit measures?

Goodness-of-fit measures are used to assess how well the explanatory variables explain the variation in the response variable.

In the following table, individuals are cross-classified by their age group and income level. Income Age. Low. Medium. High 21-35. 120. 100. 75 36-50. 150. 160. 100 51-65. 160 180. 160 To test that age group and income are independent, the null and alternative hypothesis are _________________________________________________________________________.

H0: Age group and income are independent; HA: Age group and income are dependent

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Male. Female Candidate A. 150. 130 Candidate B. 100. 120 To test that gender and candidate preference are independent, the null hypothesis is ___________________________.

H0: Gender and candidate preference are independent

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race. Coordinator. Analyst. Manager. Director White. 32. 20. 25. 9 Black. 35. 10. 25 5 Hispanic. 32. 15. 13. 2 Asian. 10. 11. 10. 0 To test that race and seniority are independent, the null and alternative hypothesis are _______________________________________________________________________.

H0: Race and seniority are independent; HA: Race and seniority are dependent

1.a) A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South(4) sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below. Source of Variation. SS. df. MS. F Between groups 87.79. 3. 29.26. 9.12 Within groups. 64.17. 20. 3.21 Total 151.96. 23 The competing hypotheses about the mean crime rates are _______.

H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. A CHART The competing hypotheses about the mean commute times are _______.

H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal

4.a) Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. A CHART You would like to determine whether an investment in Tiffany's is riskier than the market. When conducting this test, you set up the following competing hypotheses: ________.

H0:β ≤ 1; HA:β > 1

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________.

H0:β1 = 0

7.b) A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0 + β1Age + ε. The following table summarizes a portion of the regression results. A CHART When defining whether age is significant in explaining happiness, the competing hypotheses are ________.

H0:β1 = 0; HA:β1 ≠ 0

1.a) A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model:Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. A CHART Which of the following are the competing hypotheses used to test whether Advertising is significant in predicting Sales?

H0:β1 = 0; HA:β1 ≠ 0.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a one-to-one relationship between xand y, the null hypothesis takes the form ________.

H0:β1 = 1

2.a) A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β0 + β1 Double Faults + β2 Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. A CHART When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________.

H0:β1 = β2 = 0

6.a) A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model: Rent = β0 + β1 Bedroom + β2 Bath + β3Sqft + ε. The following table shows a portion of the regression results. A CHART When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________.

H0:β1 = β2 = β3 = 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________.

HA:β1 < 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ________.

HA:β1 > 0

Which of the following statements about regression analysis is FALSE?

It can establish cause-and-effect relationships.

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. A CHART Is x significantly related to y at the 5% significance level?

No, because the p-value of 0.0745 is greater than 0.05.

Which of the following is the assumption that is not applicable for a one-way ANOVA test?

The population standard deviations are not all equal.

Which of the following statements is TRUE about tests of significance to determine whether there is evidence of a linear relationship between the response variable and the explanatory variables?

The test of individual significance is the same as the test of joint significance for a simple linear regression model.

Which of the following is an example in which a one-way ANOVA test is appropriate?

To determine if mean test scores differ between the four sections.

Which of the following is an example of a chi-square test for independence?

To determine whether the likelihood of college admission depends on the race of the applicants.

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples.

True

The variability due to chance, also known as the within-treatments variance, is the estimate of σ2 which is not based on the variability _______.

between the sample means

Consider the following sample regression equation yˆy^⁢ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ________.

decrease by 60,000

Unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression ________.

indicates whether the slope of the regression line is positive or negative

When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a ________.

lower standard error of the estimate and a higher adjusted coefficient of determination

4.c) Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. A CHART When testing whether there are abnormal returns, the conclusion to the test is at the 5% significance level is to ________

not reject H0, we cannot conclude there are abnormal returns

A sample of 200 monthly observations is used to run a simple linear regression: Returns = β0 + β1 Leverage + ε. A 5% level of significance is used to study if leverage has a significant influence on returns. The value of the test statistic for the regression coefficient of Leverage is calculated as t198 = −1.09, with an associated p-value of 0.2770. The correct decision is to ________.

not reject the null hypothesis; we cannot conclude that leverage significantly explains returns

Excel and virtually all other statistical packages report the p-value ________.

or a two-tailed test that assesses whether the regression coefficient differs from zero

The R2 of a multiple regression of y on x1 and x2 measures the ________.

percentage of the variation in y that is explained by the sample regression equation

The one-way ANOVA null hypothesis is rejected when the _______.

ratio of the within-treatments variance and the between-treatments variance is significantly greater than 1

3.a) The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. When testing whether the explanatory variables are jointly significant at the 5% significance level, the conclusion is to ________.

reject H0, and conclude that the explanatory variables are jointly significant

1.b) A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model:Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. A CHART When testing whether Advertising is significant at the 10% significance level, the conclusion is to ________.

reject H0; we can conclude advertising is significant

4.b) Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. A CHART When testing whether the beta coefficient is significantly greater than one, the relevant critical value at the 5% significance level is t0.05,58 = 1.672. The conclusion to the test is to ________.

reject H0; we can conclude that the return on Tiffany stock is riskier than the return on the market

The between-treatments variance is based on a weighted sum of squared differences between the _______.

sample means and the overall mean of the data set

Simple linear regression analysis differs from multiple regression analysis in that ________.

simple linear regression uses only one explanatory variable

For the chi-square test of a contingency table, the expected cell frequencies are found as eij=(Rowitotal)(Columnjtotal)/Samplesize. which is the same as ___________________________.

the cell probability multiplied by the sample size

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. A CHART Based on the sample standard deviation, the one-way ANOVA assumption that is likely not met is _______.

the population standard deviations are assumed to be equal.

Consider the following sample regression equation yˆy^ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if ________.

the price of Product A increases by $1, then we predict the demand to decrease by 20,000

Consider the following sample regression equation yˆy^⁢ = 200 + 10x, where y is the supply for Product A (in 1,000s) and x is the price of Product A (in $). The slope coefficient indicates that if ________.

the price of Product A increases by $1, then we predict the supply to increase by 10,000

For the chi-square test of a contingency table, the expected cell frequencies are found as ________________.

the row total multiplied by the column total divided by the sample size

The standard error of the estimate measures ________.

the standard deviation of the random error

The standard error of the estimate measures ________.

the variability of the observed y-values around the predicted y-values

The chi-square test of a contingency table is a test of independence for __________________.

two qualitative variables

The coefficient of determination R2 is ________.

usually higher than adjusted R2

Consider the following simple linear regression model: y = β0 + β1x + ε. The explanatory variable is ________.

x

3.b) The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

x1 and x2

Consider the following simple linear regression model: y = β0 + β1 + ε. The response variable is ________.

y